ACTG 323 - Fluconazole is one of the most commonly prescribed drugs to treat thrush and other yeast infections. It is still not known how much fluconazole to give and how often to give it to prevent thrush from recurring in HIV-infected persons who have had thrush in the past. The main purpose of this study is to determine whether it is better to give subjects fluconazole to prevent thrush from coming back or to wait and treat each episode of thrush. The study will also look at: 1) The effect of each strategy on the development of thrush in other places, such as in the esophagus and the vagina; 2) Conditions or factors that put HIV-infected persons at risk for developing yeast infections and yeast infections that do not respond to fluconazole; 3) What happens to people who don't respond to treatment with fluconazole;, and 4) The effect of each strategy on the quality of subjects' lives. At least 948 people will be enrolled from more than 60 study centers across the country. The study will last until the last volunteer enrolled has completed the study.